A Fuzzification of Morphological Wavelets Based on Fuzzy Relational Calculus and its Application to Image Compression/Reconstruction
Hajime Nobuhara, and Kaoru Hirota
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
Received:September 25, 2003Accepted:March 29, 2004Published:July 20, 2004
Keywords:fuzzy relation, ordered structure, image compression/reconstruction, morphological wavelets
A new style of fuzzy wavelets is proposed by the fuzzification of morphological wavelets. Due to the correspondence of the morphological wavelets operations and fuzzy relational ones, wavelets analysis/synthesis schemes can be formulated based on fuzzy relational calculus. To enable efficient image compression/reconstruction, the concept of the alpha-band which is an alpha-cut generalization, is also proposed for thresholding wavelets. In an image compression/reconstruction experiment using test images extracted from the Standard Image DataBAse (SIDBA), it is confirmed that the root mean square error (RMSE) of the proposed soft thresholding is decreased to 87.3% of conventional hard thresholding, when the original image is "Lenna."
Cite this article as:H. Nobuhara and K. Hirota, “A Fuzzification of Morphological Wavelets Based on Fuzzy Relational Calculus and its Application to Image Compression/Reconstruction,” J. Adv. Comput. Intell. Intell. Inform., Vol.8 No.4, pp. 373-378, 2004.Data files: